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AN55
Application Note
Design Notes for a 2-Pole Filter
by Steven Green
R4 R1 R3
C5
_ C2 +
Figure 1. 2-Pole Low-Pass Filter
Introduction The recommended application of the CS4327, discussed in the CS4327 data sheet, requires a second-order analog filter to reduce the out-of-band noise produced by the delta-sigma modulator. The circuit shown in Figure 1 is the second-order analog filter implemented on the CS4327 evaluation board, CDB4327. This application note outlines the design steps required to determine filter component values.
Crystal Semiconductor Corporation P.O. Box 17847, Austin, TX 78760 (512) 445-7222 FAX 445-7581 http://www.crystal.com
Design Steps Step 1: Determine the required pass band gain, Ho. The output level for the CDB4327 is 2Vrms to be compatible with standard consumer audio levels. This required Ho equal to -2. Notice that Ho is also negative due to the inverting op-amp configuration.
Copyright (c) Crystal Semiconductor Corporation 1995 (All Rights Reserved)
DEC '95 AN55REV1 1
Design Notes for a 2-Pole Filter
R4
C5
Step 4: Given Fc, Ho, C2, C5, and , calculate R1, R2 and R3 using the following equations. Ho will be a negative number due to the inverting op-amp. =
R1
R3
_ +
+ 2
2
C2
o = 2Fc 2 2 + K= C5 C2 1 o C2 [ 2 - K(1 - Ho)]
Figure 2. Multiple-Feedback Low-Pass Filter
Step 2: Select the desired filter type, Butterworth, Bessel, etc. and the corner frequency, Fc, for the final design. The filter response and corner frequency determine the audio band phase and amplitude response. The filter type determines the pole-locations and therefore and . Table 1 lists the normalized pole locations for several filter types.
FILTER TYPE Butterworth Bessel 0.01 dB Chebyshev 0.1 dB Chebyshev 0.7071 1.1030 0.6743 0.6104 0.7071 0.6368 0.7075 0.7106
R3 =
R4 = R1 =
2 - K(1 - Ho ) o C5
R4 (-Ho)
Table 1. Normalized Pole Locations
Step 3: Select standard values for C5 and C2. Notice in Step 4 that K (C5/C2) and Ho must be selected such that
2 - K (1 - H o) is real.
Step 5: It is recommended that R1 be a minimum of 10 kohm to meet the CS4327 load requirements. However, values larger than 10 kohm can lead to small capacitor values (ten's of picofarads) where stray capacitance can be an appreciable amount of the total circuit capacitance. It may be necessary to adjust the capacitor values chosen in Step 3 to minimize the effects of stray capacitance and meet the minimum load requirement. Step 6: The resistor values calculated in Step 4 are generally not standard values. Select standard values which are nearest the calculated values. This should not create a large change in the filter characteristics since metal film resistors are available in approximately 2.5% increments which allows for component selection near the calculated values.
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AN55REV1
Design Notes for a 2-Pole Filter
Design Example The following example shows the steps required to duplicate the CDB4327 filter. Step 1: The desired output level is 2 Vrms which requires a pass band gain, Ho, of -2. Step 2: A two-pole Butterworth with a corner frequency of 50 kHz was selected for this application. This filter attenuates the signal at 20 kHz by approximately 0.1 dB and has nearly ideal phase linearity within the audio band. Though popular for audio applications, a Bessel response will achieve negligible phase improvement at the expense of degraded amplitude response for this application. Fc = 50 kHz = .7071 , = .7071 Step 3: Select standard values for C5 and C2. C5 = 150 pF C2 = 1000 pF Step 4: Given Fc, Ho, C2, C5, and , calculate R1, R3 and R4. R1 = 9.875 kohm R3 = 3.42 kohm R4 = 19.75 kohm Step 5: Verify that R1 is greater than or equal to 10 kohm. R1 = 10 kohm Step 6: Select standard values which are nearest the calculated values. R1 = 10 kohm R3 = 3.4 kohm R4 = 20 kohm
20 k 150 pF
10 k 1000 pF
3.4 k
_ +
Figure 4. Filter Design
References [1] C. L. Lindquist, "Active Network Design with Signal Filtering Applications", Steward & Sons [2] A. B. Williams, "Electronic Filter Design Handbook", McGraw-Hill [3] "Reference Data for Radio Engineers" (Fourth Edition), International Telephone and Telegraph Corporation [4] CS4327 Data sheet DS190PP1, Crystal Semiconductor [5] CDB4327 Data sheet DS190DB1, Crystal Semiconductor
AN55REV1
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